The right plot of Figure REF  shows the estimated 2-loop RG evolution of the ratios \(y_\tau /y_b\)  and \(y_\mu /y_s\)  in the SM with an additional contribution of the 33 element of the neutrino Yukawa matrix \(y_{\nu _3}\) . To draw this plot, we performed an MCMC analysis varying the SM parameters around their central experimental values, taken from [1]}, and weighting the points according to the \(\chi ^2\) -function. For the contribution of the 33 element of the neutrino Yukawa matrix \(y_{\nu _3}\)  we took the light neutrino mass \(m_{\nu _3}\approx 50.14\,\) meV and computed its RG evolution from the low scale up to the right-chiral neutrino mass scale \(M_3\)  (which we also varied in the MCMC analysis) according to the following (1-loop) equation [2]}:
\(\begin{split}16\pi ^2\mu \frac{d m_{\nu _3}}{d\mu }=[\alpha -3 y_\tau ^2\cos ^2(\theta _{13}^{\text{PMNS}})\cos ^2(\theta _{23}^{\text{PMNS}})]m_{\nu _3},\end{split}\) 
